Measured Games · Paper 10 of 07 · Resource economics

The common pool

After H. S. Gordon (1954) and M. B. Schaefer (1954); institutional response from E. Ostrom (1990)

Abstract

Harvesters draw from a renewable stock whose growth depends on its own size. Each additional unit of effort yields a private return while reducing the stock available to everyone, so open access drives effort upward until rent is entirely dissipated. Because stock growth is humped rather than monotone, the resulting equilibrium can sit past the point of maximum sustainable yield, where further effort lowers the catch and collapse becomes possible.

Keywordsrent dissipation · renewable stock · maximum sustainable yield · open access · governance

1Setup

Setup

A stock of fish, timber or groundwater renews itself at a rate that depends on how much of it there is. Harvesters draw from it independently. Each unit of effort a harvester adds returns a catch to that harvester and reduces the stock available to everyone, including to the same harvester next season.

Two features do the work here and neither is present in a static commons. First, the resource has its own dynamics, so today's harvest changes tomorrow's productivity. Second, growth is humped rather than monotone: a stock that is too small grows slowly because there is little of it, and a stock near capacity grows slowly because it is crowded. Between those lies a maximum. Nothing stops open access driving the stock past it.

2The model

The model

# logistic stock growth with harvest, Gordon (1954) and Schaefer (1954) dS/dt = r S ( 1 - S/K ) - q E S S stock, K carrying capacity, r intrinsic growth, E total effort, q catchability # maximum sustainable yield sits at half of capacity SMSY = K/2 HMSY = rK/4 # under open access, effort enters while any rent remains, so it stops # only when revenue per unit effort equals its cost w S(open access) = w / (p q) rent = 0 # a sole owner stops earlier, where marginal rent is zero S(sole owner) = (K/2)(1 + w/(p q K))

The open-access stock does not depend on r or K at all. It is set entirely by the price of the catch and the cost of effort. Make the resource more valuable, or fishing cheaper, and the equilibrium stock falls. If w/(pq) lands below K/2, open access settles past maximum sustainable yield, on the part of the curve where adding effort lowers the catch.

Figure 1Coupled stock and effort dynamics

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Stock and effort over time

Sustainable yield against stock · hover to read any point on the curve

Stock Effort Sustainable yield Maximum sustainable yield

Charts are focusable. With a chart focused, use the left and right arrow keys to read values along the horizontal axis.

Price of catch

Cost per unit effort

Intrinsic growth r

Entry speed

Governance

Stock—

Open-access stock—

Catch—

Max sustainable yield—

Rent—

Season0

Figure 1. Stock and effort are integrated together, so the equilibrium the run settles on is produced by the dynamics rather than looked up. Open access lets effort enter while rent is positive; sole owner holds effort at the rent-maximising level. Two things to try: raise the price and watch the open-access stock fall without any change to the biology, and push cost down until the equilibrium crosses to the left of the yield peak, where more effort buys less fish.

3Results

Results

Gordon (1954) gave the economic half and Schaefer (1954) the biological half, and together they produce the result that open access dissipates the whole of the resource rent. Effort enters while any profit remains, so in equilibrium there is none: the fishery supports its participants at exactly their opportunity cost and returns nothing to anyone as owner of the stock.

The comparative statics are the useful part. Because the bionomic equilibrium sits at w/(pq), a rise in price or a fall in fishing cost lowers the equilibrium stock, and a more productive fishery, higher r or K, does not protect it. Technology that makes harvesting cheaper is therefore a threat to the stock rather than a benefit to it, which is not how fishing technology is usually discussed.

The humped yield curve adds the failure mode. Left of the peak, a smaller stock produces a smaller catch, so effort and stock can spiral down together. Ostrom (1990) is the standard response, documenting long-lived community institutions that avoid the open-access equilibrium without either privatisation or state control, by defining boundaries, monitoring and graduated sanctions.

4Evidence

Evidence

The Gordon-Schaefer model is the workhorse of fisheries economics and the surplus-production form underlies a great deal of stock assessment. Its qualitative prediction, that unregulated fisheries end up overcapitalised and rent-free, is among the better supported claims in resource economics: the World Bank and FAO Sunken Billions assessment estimated tens of billions of dollars in forgone annual rent from global marine fisheries relative to a rebuilt and better-managed alternative.

The Northern cod collapse off Newfoundland is the case usually cited for the left-hand side of the yield curve. Landings peaked and then fell steeply through the late 1980s, and a moratorium was declared in 1992; the stock has not returned to anything like its former biomass in the decades since, which is evidence that a depleted stock does not simply climb back up the curve it came down.

Ostrom (1990) supplies the counter-evidence to the pessimistic reading. Across irrigation systems, alpine pastures, forests and inshore fisheries she documented long-enduring common-property regimes that sustained their resources for centuries, and identified the design principles those regimes shared.

5Limitations

Limitations

Logistic growth is a caricature. Real stocks have age structure, recruitment that depends on spawning biomass in complicated ways, and environmental variation that can swamp the deterministic signal. Single-species models also ignore the rest of the ecosystem, and the catchability coefficient q is usually the least reliable number in the whole assessment.

The economics is equally simplified. Effort is treated as homogeneous and instantly adjustable, prices are fixed, and there is no discounting in the version implemented above, which matters because a sole owner with a high discount rate can rationally choose to deplete a slow-growing stock.

Most importantly, the model's open-access case is a benchmark, not a description. Ostrom's central empirical point is that unregulated open access is comparatively rare, and that treating every commons as headed for the bionomic equilibrium mistakes a limiting case for the normal one.

References

Gordon, H. S. (1954). The economic theory of a common-property resource: The fishery. Journal of Political Economy, 62(2), 124–142. https://doi.org/10.1086/257497
Hardin, G. (1968). The tragedy of the commons. Science, 162(3859), 1243–1248. https://doi.org/10.1126/science.162.3859.1243
Ostrom, E. (1990). Governing the commons: The evolution of institutions for collective action. Cambridge University Press. https://doi.org/10.1017/CBO9780511807763
Ostrom, E., Burger, J., Field, C. B., Norgaard, R. B., & Policansky, D. (1999). Revisiting the commons: Local lessons, global challenges. Science, 284(5412), 278–282. https://doi.org/10.1126/science.284.5412.278
Schaefer, M. B. (1954). Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Bulletin of the Inter-American Tropical Tuna Commission, 1(2), 27–56.
Worm, B., Hilborn, R., Baum, J. K., Branch, T. A., Collie, J. S., Costello, C., Fogarty, M. J., Fulton, E. A., Hutchings, J. A., Jennings, S., Jensen, O. P., Lotze, H. K., Mace, P. M., McClanahan, T. R., Minto, C., Palumbi, S. R., Parma, A. M., Ricard, D., Rosenberg, A. A., ... Zeller, D. (2009). Rebuilding global fisheries. Science, 325(5940), 578–585. https://doi.org/10.1126/science.1173146

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